What are the four scenarios for interactive graph drawing?

Papakostas and Tollis [30] have defined four scenarios for interactive orthogonal graph drawing, namely, Draw-From-Scratch, Full-Control, No-Change, and Relative-Coordinates, that formalize four ways by which a new drawing can be interactively constructed.

What is the explanation for the poor performance of Bend-Stretch?

The poor experimental performance of Bend-Stretch can be explained by noting that the edges involved in crossings are decomposed by the planarization phase into several fragments, and the bound of two bends per edge applies separately to each fragment.

What is the way to compute the minimum crossing number?

When the permutation of the vertices on one layer is fixed, the exact minimum crossing number can be efficiently computed in practice, so there is no real need for heuristics.

Why are layering-based algorithms popular among the designers of practical graph drawing systems?

Because of their generality and conceptual simplicity, these algorithms are very popular among the designers of practical graph drawing systems.

What is the screen ratio of the drawings produced by the four algorithms?

The screen ratio of the drawings produced by the four algorithms changes very slowly with n for n > 50, and might indicate a convergence to some stable value.

How many times has MagneticSpring been run on the test graphs?

For each type of magnetic field, MagneticSpring has been repeatedly run on the test graphs with increasing values of the magnetic field strength.

How do the authors improve the results of Bend-Stretch, Pair, and Column?

the authors believe that some results for Bend-Stretch, Pair, and Column can be improved since the three algorithms all need to transform the input graph into a directed acyclic graph, and they do so by means of an st-numbering.

What is the first study of the restricted version of the 2-layer crossing minimization problem?

The authors first study the restricted version of the 2-layer crossing minimization problem where the permutation of the vertices on one layer is fixed.

What are the two authors using for constructing hierarchical drawings?

Newbery Paulish and Tichy [57], and Bohringer and Newbery Paulish [58] have used the algorithm of Sugiyama et al. [31] for constructing hierarchical drawings that maintain the relative ordering of vertices assigned to the same horizontal layer in successive drawings.

Open AccessJournal Article10.1002/1097-024X(200009)30:11<1235::AID-SPE339>3.0.CO;2-B

Experimental studies on graph drawing algorithms

Luca Vismara, +5 more

- 01 Sep 2000

- Software - Practice and Experience

- Vol. 30, Iss: 11, pp 1235-1284

TL;DR: The results of some of the most popular experimental studies on graph drawing algorithms are described, each of which presents an in‐depth comparative analysis on a specific class of algorithms, namely, algorithms for orthogonal drawings, interactive algorithms, algorithm for hierarchical drawings, and force‐directed and randomized algorithms.

Abstract: Graph drawing plays an important role in the solution of many information visualization problems. Most of the graph drawing algorithms are accompanied by a theoretical analysis of their characteristics, but only extensive experimentations can assess the practical performance of graph drawing algorithms in real‐life applications. In this paper, we describe the results of some of the most popular experimental studies on graph drawing algorithms. Each study presents an in‐depth comparative analysis on a specific class of algorithms, namely, algorithms for orthogonal drawings, interactive algorithms, algorithms for hierarchical drawings, and force‐directed and randomized algorithms. Copyright © 2000 John Wiley & Sons, Ltd.

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Most frequently asked questions

1. What type of springs can be used to model edges?

In particular, edges can be modeled with three types of springs: non-magnetic springs, unidirectional magnetic springs, and bidirectional magnetic springs.

2. What is the problem of recognizing isomorphic graphs?

Then they noted that many directed graphs were isomorphic; since the vertices of the directed graphs have labels associated with them, the problem of recognizing isomorphic graphs is tractable.

3. What is the attractive aspect of graph drawing algorithms based on force-directed methods?

One of the most attractive aspects of graph drawing algorithms based on force-directed methods is the variety of possible applications, since they can be used for drawing general undirected graphs.

4. How does the authors think the length of the longest edge can be reduced?

The authors believe that the length of the longest edge can be reduced for Bend-Stretch, Pair, and Column by implementing the st-numbering procedure based on a breadth-first search.

Figure 4. Comparison chart forTime (seconds): thex-axis indicates the number of vertices.

Figure 18. Comparison charts forTime (seconds),LengthRatio, andUnifLength relative to the mixed graphs: thex-axes indicate the number of vertices plus the number of edges. (Data courtesy of Franz J. Brandenburg, Michael Himsolt and Christoph Rohrer.)

Figure 10. Comparison charts forTime (seconds) andCrossings in the third experiment relative to the two-sided crossing minimization problem: thex-axes indicate the number of vertices. (Data courtesy of Michael J¨unger and Petra Mutzel.)

Figure 7. Comparison charts forTime (seconds) andCrossings in the first experiment relative to the one-sided crossing minimization problem: thex-axes indicate the density of the graph. (Data courtesy of Michael J¨unger and Petra Mutzel.)

Figure 3. Comparison charts forTotalLength,MaxLength, andUnifLength: thex-axes indicate the number of vertices.

Citations

•Journal Article

The Barycenter Heuristic and the Reorderable Matrix

Erkki Mäkinen, +1 more

- 01 Jan 2005

- Informatica (slovenia)

TL;DR: The purpose of this paper is to discuss the role of the barycenter heuristic in ordering the rows and columns of the matrix and survey its use in various contexts and recall the theoretical results obtained.

...read moreread less

•Journal Article

An experimental study of crossing minimization heuristics

Carsten Gutwenger, +1 more

- 01 Jan 2003

- Lecture Notes in Computer Science

TL;DR: The effects of various methods for computing a maximal planar subgraph and for edge re-insertion including post-processing and randomization are studied.

...read moreread less

•Book Chapter•10.1007/978-3-540-24595-7_2

An Experimental Study of Crossing Minimization Heuristics

Carsten Gutwenger, +1 more

- 21 Sep 2003

TL;DR: In this article, the authors present an extensive experimental study of heuristics for crossing minimization based on the planarization approach, which is the most successful framework for crossing optimization.

...read moreread less

•Journal Article•10.1007/S10796-015-9591-0

New knowledge in strategic management through visually mining semantic networks

Gurdal Ertek, +3 more

- 01 Feb 2017

- Information Systems Frontiers

TL;DR: A three-stage framework is proposed and described that can enable managers to develop a deeper understanding of the strategic management domain, and expand on existing knowledge through visual analysis, and support a case study that involves unstructured knowledge of profit patterns and the related strategies to succeed using these patterns.

...read moreread less

•Book Chapter•10.1007/978-3-642-25878-7_24

Overloaded orthogonal drawings

Evgenios M. Kornaropoulos, +1 more

- 21 Sep 2011

TL;DR: Overloaded Orthogonal drawings present several interesting properties such as efficient visual edge confirmation as well as simplicity and clarity of the drawing.

...read moreread less

...

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References

Journal Article•10.1002/SPE.4380211102

Graph drawing by force-directed placement

Thomas M. J. Fruchterman, +1 more

- 01 Nov 1991

- Software - Practice and Experience

TL;DR: A modification of the spring‐embedder model of Eades for drawing undirected graphs with straight edges is presented, developed in analogy to forces in natural systems, for a simple, elegant, conceptually‐intuitive, and efficient algorithm.

...read moreread less

5.8K

Journal Article•10.1016/0020-0190(89)90102-6

An algorithm for drawing general undirected graphs

Tomihisa Kamada, +1 more

- 12 Apr 1989

- Information Processing Letters

3.1K

Journal Article•10.1109/TSMC.1981.4308636

Methods for Visual Understanding of Hierarchical System Structures

Kozo Sugiyama, +2 more

- 01 Feb 1981

TL;DR: Two kinds of new methods are developed to obtain effective representations of hierarchies automatically: theoretical and heuristic methods that determine the positions of vertices in two steps to improve the readability of drawings.

...read moreread less

1.4K

A Heuristic for Graph Drawing

Peter Eades

- 01 Jan 1984

TL;DR: Researchers propose a heuristic method for graph drawing, presenting a successful approach to visually representing complex networks, with implications for various fields, including computer science, mathematics, and information visualization.

...read moreread less

1.3K

•Journal Article•10.1016/0925-7721(94)00014-X

Algorithms for drawing graphs: an annotated bibliography

Giuseppe Di Battista, +3 more

- 01 Aug 1988

- Computational Geometry: Theory and Appli...

TL;DR: A bibliographic survey on algorithms whose goal is to produce aesthetically pleasing drawings of graphs is presented, a first attempt to encompass both theoretical and application-oriented papers from disparate areas.

...read moreread less

...

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Experimental studies on graph drawing algorithms

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AI Agents for this Paper

Most frequently asked questions

1. What type of springs can be used to model edges?

2. What is the problem of recognizing isomorphic graphs?

3. What is the attractive aspect of graph drawing algorithms based on force-directed methods?

4. How does the authors think the length of the longest edge can be reduced?

5. What are the four scenarios for interactive graph drawing?

6. What is the explanation for the poor performance of Bend-Stretch?

7. What is the way to compute the minimum crossing number?

8. Why are layering-based algorithms popular among the designers of practical graph drawing systems?

9. What is the screen ratio of the drawings produced by the four algorithms?

10. How many times has MagneticSpring been run on the test graphs?

11. How do the authors improve the results of Bend-Stretch, Pair, and Column?

12. What is the first study of the restricted version of the 2-layer crossing minimization problem?

13. What are the two authors using for constructing hierarchical drawings?

Figures

Citations

The Barycenter Heuristic and the Reorderable Matrix

An experimental study of crossing minimization heuristics

An Experimental Study of Crossing Minimization Heuristics

New knowledge in strategic management through visually mining semantic networks

Overloaded orthogonal drawings

References

Graph drawing by force-directed placement

An algorithm for drawing general undirected graphs

Methods for Visual Understanding of Hierarchical System Structures

A Heuristic for Graph Drawing

Algorithms for drawing graphs: an annotated bibliography

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